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Search: id:A088368
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| A088368 |
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G.f. satisfies A(x) = sum(n=0,infinity, n!*(x*A(x))^n ). |
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1
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| 1, 1, 3, 13, 69, 421, 2867, 21477, 175769, 1567273, 15213955, 160727997, 1846282381, 23013527421, 310284575683, 4506744095141, 70199956070705, 1167389338452753
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = number of partitions of [n] into sets of noncrossing lists. For example, a(4) = 69 counts the 73 partitions of [n] into sets of lists (A000262) except for 13-24, 13-42, 31-24, 31-42 which are crossing. - David Callan (callan(AT)stat.wisc.edu), Jul 25 2008
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LINKS
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David Callan, Sets, Lists and Noncrossing Partitions .
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EXAMPLE
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A(x) = 1 + xA(x) + 2!(xA(x))^2 + 3!(xA(x))^3 + 4!(xA(x))^4 + ...
=1+x(1+x+3x^2+13x^3+..)+2!x^2(1+2x+7x^2+..)+3!x^3(1+3x+..)+4!x^4(1+..)+..
=1 + x + 3x^2 + 13x^3 + 69x^4 +...
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MATHEMATICA
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FrequencyDistribution[list_List] := Module[{set = Union[list]}, Table[{set[[i]], Count[list, set[[i]]]}, {i, Length[set]}]]; a[0] = 1; a[n_]/; n>=1 := a[n] = Apply[Plus, Module[{frequencies}, Map[(frequencies=Map[Last, FrequencyDistribution[ # ]]; Sum[frequencies]!*Apply[Multinomial, frequencies]* Product[Map[a, # ]])&, Partitions[n]-1 ]]] Table[a[n], {n, 0, 15}] - David Callan (callan(AT)stat.wisc.edu), Jul 25 2008
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CROSSREFS
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Sequence in context: A153395 A067145 A088714 this_sequence A007808 A104989 A119906
Adjacent sequences: A088365 A088366 A088367 this_sequence A088369 A088370 A088371
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Sep 28 2003
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